In a vernier callipers, one main scale division is x cm and n divisions of the vernier scale coincide with (n-1) divisions of the main scale. The least count (in cm ) of the callipers is

Question

In a vernier callipers, one main scale division is x cm and n divisions of the vernier scale coincide with (n-1) divisions of the main scale. The least count (in cm ) of the callipers is (A) ((n-1/n)) x (B) (n x/(n-1)) (C) (x/n) (D) (x/(n-1))

Tardigrade Admin · Accepted Answer

Vernier constant = value of 1 M.S.D. - value of 1 V.S.D. Now n V.S.D. =(n-1) text M.S.D. =(n-1) x cm ∴ 1 V.S.D. =((n-1/n)) x cm ∴ V . C .=x cm -((n-1/n)) x cm =(x/n) cm

Q. In a vernier callipers, one main scale division is $x c m$ and $n$ divisions of the vernier scale coincide with $(n - 1)$ divisions of the main scale. The least count (in $c m$ ) of the callipers is

$(\frac{n - 1}{n}) x$

$\frac{n x}{( n - 1 )}$

$\frac{x}{n}$

$\frac{x}{( n - 1 )}$

Vernier constant = value of $1 M . S . D$ . - value of $1 V . S . D$ .
Now $n$ V.S.D. $= (n - 1) M.S.D.$
$= (n - 1) x c m$
$∴ 1 V . S . D . = (\frac{n - 1}{n}) x c m$
$∴ V . C . = x c m - (\frac{n - 1}{n}) x c m$
$= \frac{x}{n} c m$

Q. In a vernier callipers, one main scale division is xcm and n divisions of the vernier scale coincide with (n−1) divisions of the main scale. The least count (in cm ) of the callipers is

(nn−1​)x

(n−1)nx​

nx​

(n−1)x​